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Introduction to Scientific and Engineering Computing BIL106E (F)


Top-Down Programming

 The task of writing a program can be analyzed in four basic steps:

1-) Specify the problem clearly, (not subject of this course), specification,

2-) Analyze the problem and break it down into its fundamental sub-elements

analysis and design,

3-) Code the program according to the plan developed at step 2 coding,

4-) Test the program for all situations that you can envisage, testing.
 Top-down design involves refining the problem into successively greater level of detail. The programming of sub-problems identified during top-down design can be deferred by specifying a sub-program for the purpose.
Example: 1-) Problem specification: Write a program that asks for x and y

coordinates of three points and that calculate the equation of the circle passing through those three points, namely,


and then display the coordinates (a,b) of the centre of the circle and its radius, r.

2-) Analysis: a) Read three sets of coordinates (x1,y1), (x2,y2) and (x3,y3),

b) Calculate the equation of the circle (x-a)2+(y-b)2=r2

using the procedure calculate_circle

c) Display the coordinates (a,b) and the radius r.

3-) Coding: program Circle

! This program calculates the equation of a circle passing

! through three points

! Variable declarations

real :: x1,y1,x2,y2,x3,y3,a,b,r

!Step 1

print *,”Please type the coordinates of three points”

print *,”in the order x1,y1,x2,y2,x3,y3”

read *, x1,y1,x2,y2,x3,y3 !Read three points

!Step 2

call calculate_circle(x1,y1,x2,y2,x3,y3,a,b,r)

!Step 3

print *,”The centre of the circle through these points”, &

“is (“,a,”,”,b,”)”

print *,”Its radius is”,r

end program Circle
After running the code, the followings will appear on the screen,

Please type the coordinates of three points

in the order x1,y1,x2,y2,x3,y3

4.71 4.71

6.39 0.63

0.63 3.06

The centre of the circle through these points is (3.502, 1.827)

Its radius is 3.126

Simulation of natural/artificial systems

Build a conceptual quantitative model (most of the time, write down the appropriate equations),

Formulate a solution to these equations using numerical methods

Data structures + algorithms,

Program these data structures and algorithms in a language,

Run the program and analyze its output using visualization techniques.

Some Basic Concepts in Fortran (F)

 Program=Data Types + Algorithms

Data types: what you work on, Algorithms: what you do with them.

Structure of a program (in Fortran 90)

Heading (program, module, etc.)

Specification part

Execution part

Subprogram part

End program statement

 Specification statements provide information about the program to the compiler.

 Execution statements are obeyed by the computer during the execution of the


 Use exclamation (!) mark comments (ignored by the computer) often in your


 There are some limits on for F names and identifiers such as:

Each line may have a maximum of 132 characters. Each identifier must consist of a maximum of 31 characters. 39 maximum line for every statement. (Those change from compiler to compiler that you use.)


Names used to identify programs, constants, variables, etc.

Identifiers must begin with a letter. This can be followed by up to 30 letters, digits, underscores. Be careful with the case: lower or upper case letters. Examples: Current, Decay_Rate, pressure, an_identifier_with_a_long_name, the_best_program

Errors in F

 Syntactic (Grammatical) Erros and Semantic (Logical) Errors. Syntactic errors are easier to find and to correct than the semantic ones.

Example: The dat sat on the mat, (dat has no meaning, word is wrong)

The cat sat the on mat, (grammer is incorrect, words are valid)

The above both sentences in natural English have syntactic errors.

The mat sat on the cat, (grammer is correct, words are valid), the sentence

has no meaning, so it has semantic error. The correct sentence can be as follows:

The cat sat on the mat.
Design of Programs

 Programs should be well-designed:



easily maintained, and



name = expression

replace the content of the variable name with the result of the expression

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